I am looking for some example of any that is discontinous at at least one point but where the restriction of the function to, I quote, "every straight line in " is continous. (This is of course part of some homework, but I cannot figure it out, which is why I am asking.)
First of all, I do not really get what this last part means. Is that supposed to be some restriction to the defenition set? And if so: What kind of function could that be. Don't I again get a neighbourhood of all points if I regard all such lines? I am confused.
Thanks for any help!